Globalization and intensified volume of trade and transport around the world are accelerating the rate of biological invasions. It is therefore increasingly important to understand the processes through which invasive species colonize new habitats, often to the detriment of native flora. The initial steps of an invasion are particularly critical, as the introduced species relies on limited genetic diversity to adapt to a new environment. However, our understanding of this critical stage of the invasion is currently limited. We used a citizen science approach and social media to survey the distribution of invasive sunflower in Israel. We then sampled and sequenced a representative collection and compared it with available genomic data sets of North American wild sunflower, landraces and cultivars. We show that invasive wild sunflower is rapidly establishing throughout Israel, probably from a single, recent introduction from Texas, while maintaining high genetic diversity through ongoing gene flow. Since its introduction, invasive sunflower has spread quickly to most regions, and differentiation was detected despite extensive gene flow between clusters. Our findings suggest that rapid spread followed by continuous gene flow between diverging populations can serve as an efficient mechanism for maintaining sufficient genetic diversity at the early stages of invasion, promoting rapid adaptation and establishment in the new territory.